Review for Final Exam

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Review for Final Exam

• 15th December (Saturday)
• 130-430 PM
• LMS 151

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Part 1 Closed book and notes (30 minutes) Based
on general theoretical concepts Part 2 Open
book and notes (120 minutes) Based on numerical
problems
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Heat ExchangersDesign Considerations

• Chapter 11

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Heat Exchanger Types
Heat exchangers are ubiquitous in energy
conversion and utilization. They involve heat
exchange between two fluids separated by a solid
and encompass a wide range of flow configurations.

• Concentric-Tube Heat Exchangers

• Simplest configuration.

• Superior performance associated with counter
  flow.

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• Cross-flow Heat Exchangers

• For cross-flow over the tubes, fluid motion,
  and hence mixing, in the transverse
• direction (y) is prevented for the finned
  tubes, but occurs for the unfinned condition.

• Heat exchanger performance is influenced by
  mixing.

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• Shell-and-Tube Heat Exchangers

One Shell Pass and One Tube Pass

• Baffles are used to establish a cross-flow and
  to induce turbulent mixing of the
• shell-side fluid, both of which enhance
  convection.

• The number of tube and shell passes may be
  varied, e.g.

One Shell Pass, Two Tube Passes
Two Shell Passes, Four Tube Passes
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• Compact Heat Exchangers

• Widely used to achieve large heat rates per
  unit volume, particularly when
• one or both fluids is a gas.

• Characterized by large heat transfer surface
  areas per unit volume, small
• flow passages, and laminar flow.

(a) Fin-tube (flat tubes, continuous plate fins)
(b) Fin-tube (circular tubes, continuous plate
fins)
(c) Fin-tube (circular tubes, circular fins)
(d) Plate-fin (single pass)
(e) Plate-fin (multipass)
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Overall Heat Transfer Coefficient

• An essential requirement for heat exchanger
  design or performance calculations.

• Contributing factors include convection and
  conduction associated with the
• two fluids and the intermediate solid, as
  well as the potential use of fins on both
• sides and the effects of time-dependent
  surface fouling.

• With subscripts c and h used to designate the
  cold and hot fluids, respectively,
• the most general expression for the overall
  coefficient is

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Assuming an adiabatic tip, the fin efficiency is
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A Methodology for Heat Exchanger Design
Calculations - The Log Mean Temperature
Difference (LMTD) Method -

• A form of Newtons law of cooling may be
  applied to heat exchangers by
• using a log-mean value of the temperature
  difference between the two fluids

• Counter-Flow Heat Exchanger

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• Parallel-Flow Heat Exchanger

• Note that Tc,o cannot exceed Th,o for a PF HX,
  but can do so for a CF HX.

• For equivalent values of UA and inlet
  temperatures,

• Shell-and-Tube and Cross-Flow Heat Exchangers

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Overall Energy Balance

• Application to the hot (h) and cold (c) fluids

• Assume negligible heat transfer between the
  exchanger and its surroundings
• and negligible potential and kinetic energy
  changes for each fluid.

• Assuming no l/v phase change and constant
  specific heats,

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Special Operating Conditions

• Case (c) ChCc.

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Use of a Correction Factor
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Effectiveness NTU method

• Computational Features/Limitations of the LMTD
  Method

• The LMTD method may be applied to design
  problems for
• which the fluid flow rates and inlet
  temperatures, as well as
• a desired outlet temperature, are prescribed.

For a specified
HX type, the required size (surface area), as
well as the other outlet temperature, are
readily determined.

• If the LMTD method is used in performance
  calculations for which
• both outlet temperatures must be determined
  from knowledge of the
• inlet temperatures, the solution procedure
  is iterative.

• For both design and performance calculations,
  the effectiveness-NTU
• method may be used without iteration.

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Definitions

• Maximum possible heat rate

• Will the fluid characterized by Cmin or Cmax
  experience the largest possible
• temperature change in transit through the
  HX?

• Why is Cmin and not Cmax used in the definition
  of qmax?

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• Number of Transfer Units, NTU

• A dimensionless parameter whose magnitude
  influences HX performance

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Heat Exchanger Relations

• Performance Calculations

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• Design Calculations

• For all heat exchangers,

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Radiation Processes and Properties-Basic
Principles and Definitions-

• Chapter 12
• 12.1 through 12.8

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General Considerations

• Emission is due to oscillations and transitions
  of the many electrons that comprise
• matter, which are, in turn, sustained by the
  thermal energy of the matter.

• Emission corresponds to heat transfer from the
  matter and hence to a reduction
• in its thermal energy.

• Radiation may also be intercepted and absorbed
  by matter, resulting in its increase
• in thermal energy.

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• Emission from a gas or a semitransparent solid
  or liquid is a volumetric
• phenomenon. Emission from an opaque solid or
  liquid is treated as a surface phenomenon.

• The dual nature of radiation

• In some cases, the physical manifestations of
  radiation may be explained
• by viewing it as particles (aka photons or
  quanta).

• In other cases, radiation behaves as an
  electromagnetic wave.

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For propagation in a vacuum,
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The Electromagnetic Spectrum

• The amount of radiation emitted by an opaque
• surface varies with wavelength, and we may
• speak of the spectral distribution over all
• wavelengths or of monochromatic/spectral
• components associated with particular
  wavelengths.

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Radiation Heat Fluxes and Material Properties

• ? reflectivity ? fraction of irradiation (G)
  reflected.
• a ? absorptivity ? fraction of irradiation
  absorbed.
• t ? transmissivity ? fraction of irradiation
  transmitted through the medium.
• r a t 1 for any medium. r a 1
  for an opaque medium.

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Directional Considerations and Radiation Intensity

• In general, radiation fluxes can be determined
• only from knowledge of the directional and
• spectral nature of the radiation.

• Radiation emitted by a surface will be in all
• directions associated with a hypothetical
• hemisphere about the surface and is
• characterized by a directional distribution.

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• The solid angle associated with a complete
  hemisphere is

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Relation of Intensity to Emissive Power,
Irradiation, and Radiosity

• For a diffuse surface, emission is isotropic and

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• The radiosity of an opaque surface accounts for
  all of the radiation leaving the
• surface in all directions and may include
  contributions from both reflection and
• emission.

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• How can the intensities that appear in the
  preceding equations be quantified?

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Blackbody Radiation and Its Intensity

• The Blackbody

• An idealization providing limits on radiation
  emission and absorption by matter.

• For a prescribed temperature and wavelength, no
  surface can emit
• more radiation than a blackbody the ideal
  emitter.

• A blackbody is a diffuse emitter.

• A blackbody absorbs all incident radiation the
  ideal absorber.

• The Isothermal Cavity (Hohlraum).

(a) After multiple reflections, virtually all
radiation entering the cavity is absorbed.

• Emission from the aperture is the maximum
  possible emission achievable for
• the temperature associated with the cavity
  and is diffuse.

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• Does this condition depend on whether the
  cavity surface is highly
• reflecting or absorbing?

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The Spectral (Planck) Distribution of Blackbody
Radiation

• The spectral distribution of the blackbody
  emissive power (determined
• theoretically and confirmed experimentally)
  is

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• The fractional amount of total blackbody
  emission appearing at lower
• wavelengths increases with increasing T.

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The Stefan-Boltzmann Law and Band Emission

• The total emissive power of a blackbody is
  obtained by integrating the Planck
• distribution over all wavelengths.

where, in general,
and numerical results are given in Table 12.2.
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• If emission from the sun may be approximated as
  that from a blackbody at
• 5800 K, at what wavelength does peak
  emission occur?

• Would you expect radiation emitted by a
  blackbody at 800 K to be discernible
• by the naked eye?

• As the temperature of a blackbody is increased,
  what color would be
• the first to be discerned by the naked eye?

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Surface Emissivity

• Radiation emitted by a surface may be
  determined by introducing a property
• (the emissivity) that contrasts its emission
  with the ideal behavior of a blackbody
• at the same temperature.

• The definition of the emissivity depends upon
  ones interest in resolving
• directional and/or spectral features of the
  emitted radiation, in contrast
• to averages over all directions
  (hemispherical) and/or wavelengths (total).

• The spectral, directional emissivity

• The spectral, hemispherical emissivity (a
  directional average)

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• The total, hemispherical emissivity (a
  directional and spectral average)

• To a reasonable approximation, the
  hemispherical emissivity is equal to
• the normal emissivity.

• Representative values of the total, normal
  emissivity

• Note
• Low emissivity of polished metals and
  increasing emissivity for unpolished
• and oxidized surfaces.

• Comparatively large emissivities of
  nonconductors.

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• Representative spectral variations

• Representative temperature variations

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Response to Surface Irradiation Absorption,
Reflection and Transmission

• There may be three responses of a
  semitransparent medium to irradiation

• The wavelength of the incident radiation, as
  well as the nature of the material,
• determine whether the material is
  semitransparent or opaque.

• Are glass and water semitransparent or opaque?

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• Unless an opaque material is at a sufficiently
  high temperature to emit visible
• radiation, its color is determined by the
  spectral dependence of reflection in
• response to visible irradiation.

• What may be said about reflection for a white
  surface?

A black surface?

• Why are leaves green?

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Absorptivity of an Opaque Material

• The spectral, directional absorptivity

Assuming negligible temperature dependence,

• The spectral, hemispherical absorptivity

• To what does the foregoing result simplify, if
  the irradiation is diffuse?

If the surface is diffuse?

• The total, hemispherical absorptivity

• If the irradiation corresponds to emission from
  a blackbody, how may the
• above expression be rewritten?

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Reflectivity of an Opaque Material

• The spectral, directional reflectivity
  Assuming negligible temperature
• dependence

• The spectral, hemispherical reflectivity

• To what does the foregoing result simplify if
  the irradiation is diffuse?

If the surface is diffuse?

• The total, hemispherical reflectivity

• Limiting conditions of diffuse and
• specular reflection.

Polished and rough surfaces.
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• Is snow a highly reflective substance?

White paint?
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Transmissivity

• The spectral, hemispherical transmissivity

Assuming negligible
temperature dependence,
Note shift from semitransparent to opaque
conditions at large and small wavelengths.

• The total, hemispherical transmissivity

• For a semitransparent medium,

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Kirchhoffs Law

• Kirchhoffs law equates the total,
  hemispherical emissivity of a surface to its
• total, hemispherical absorptivity

However, conditions associated with its
derivation are highly restrictive
Irradiation of the surface corresponds to
emission from a blackbody at the same temperature
as the surface.

• But, Kirchhoffs law may be applied to the
  spectral, directional properties
• without restriction

Why are there no restrictions on use of the
foregoing equation? How might we take advantage
of the foregoing equation?
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Diffuse/Gray Surfaces
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Radiation Exchange Between SurfacesEnclosures
with Nonparticipating Media

• Chapter 13
• Sections 13.1 through 13.4

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Basic Concepts

• Enclosures consist of two or more surfaces that
  envelop a region of space
• (typically gas-filled) and between which
  there is radiation transfer.

Virtual, as well as real, surfaces
may be introduced to form an enclosure.

• A nonparticipating medium within the enclosure
  neither emits, absorbs,
• nor scatters radiation and hence has no
  effect on radiation exchange
• between the surfaces.

• Each surface of the enclosure is assumed to be
  isothermal, opaque, diffuse
• and gray, and to be characterized by uniform
  radiosity and irradiation.

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The View Factor (also Configuration or Shape
Factor)


Consider exchange between differential areas
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View Factor Relations

• Reciprocity Relation.

With

• Summation Rule for Enclosures.

• Two-Dimensional Geometries (Table 13.1)

For example,
An Infinite Plane and a Row of Cylinders
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• Three-Dimensional Geometries (Table 13.2).

For example,
Coaxial Parallel Disks
Fig. 13.5
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Blackbody Radiation Exchange
net rate at which
radiation leaves surface i due to its interaction
with j
or net rate at which surface j gains radiation
due to its interaction with i

• Net radiation transfer from surface i due to
  exchange with all (N)
• surfaces of an enclosure

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General Radiation Analysis for Exchange between
the N Opaque, Diffuse, Gray Surfaces of an
Enclosure

• Alternative expressions for net radiative
• transfer from surface i

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• Equating Eqs. (3) and (4) corresponds to a
  radiation balance on surface i

which may be represented by a radiation network
of the form
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• Methodology of an Enclosure Analysis

• Evaluate all of the view factors appearing in
  the resulting equations.

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Two-Surface Enclosures

• Simplest enclosure for which radiation exchange
  is exclusively between two
• surfaces and a single expression for the rate
  of radiation transfer may be
• inferred from a network representation of the
  exchange.

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• Special cases are presented in Table 13.3.

For example,

• Large (Infinite) Parallel Plates

• Note result for Small Convex Object in a Large
  Cavity.

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Radiation Shields

• Consider use of a single shield in a
  two-surface enclosure, such as that associated
  with
• large parallel plates

Note that, although rarely the case, emissivities
may differ for opposite surfaces of the shield.
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• Radiation Network

• The foregoing result may be readily extended to
  account for multiple shields
• and may be applied to long, concentric
  cylinders and concentric spheres,
• as well as large parallel plates.

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The Reradiating Surface

• Approximated by surfaces that are well
  insulated on one side and for which
• convection is negligible on the opposite
  (radiating) side.

• Three-Surface Enclosure with a Reradiating
  Surface

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Implications of the Simplifying Assumptions
We have assumed

• Isothermal, opaque surfaces.
• Gray surfaces.
• Diffusely emitting and reflecting surfaces.
• Surfaces that all experience uniform
  irradiation.
• Surfaces that all produce uniform radiosity.
• Enclosures with gases that do not emit, absorb,
  or scatter.

Seldom are all the assumptions rigorously
satisfied. The analysis technique may, however,
be used to obtain first estimates. The
implications of not satisfying all the
assumptions rigorously are often less severe in
problems involving multimode effects.
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Multimode Effects

• In an enclosure with conduction and convection
  heat transfer to or from
• one or more surfaces, the foregoing treatments
  of radiation exchange may
• be combined with surface energy balances to
  determine thermal conditions.

• Consider a general surface condition for which
  there is external heat addition
• (e.g., electrically), as well as conduction,
  convection and radiation.